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Algebraic Identities

What must be ...

Question

What must be added to the expression $4 x^{2} - 12 x + 7$ to make it a whole square?

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Solution

$4 x^{2} - 12 x + 7$

$(2 x)^{2} - 2 (2 x) (3) + 3^{2} - 3^{2} + 7$

$(2 x - 3)^{2} - 9 + 7$

$(2 x - 3)^{2} - 2$

$∴$ 2 must be added to the expression to make it a whole square.

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